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e.g. Friedmann-Robertson-Walker (FRW) or Robertson-Walker (RW).
The FLRW metric is used as a first approximation for the standard big bang cosmological model of the universe. Because the FLRW assumes homogenity, some popular accounts mistakenly assert that the big bang model cannot account for the observed lumpiness of the universe. In actuality, the FLRW is used as a first approximation for the evolution of the universe because it is simple to calculate, and models which calculate the lumpiness in the universe are added onto FLRW as extensions. As of 2003, the theoretical implications of the various extensions to FLRW appear to be well understood, and the goal is to make these consistent with observations from COBE and WMAP.
The metric can be written as
where a(t) is the scale factor of the universe at time t, or or for negative, zero or positive curvature respectively, and , where RC is the ( absolute value of the) radius of curvature.
In this formulation of the metric, gives the comoving distance from the observer, and gives the proper motion distance .
The solution to the FLRW metric for a fluid with constant density and pressure is given by the Friedmann equations. Most cosmologists agree that the observable part of the Universe is well approximated by an almost FLRW model, that is, a model which follows the FLRW metric apart from primordial density fluctuations. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the Universe.
However, for brevity, the almost FLRW model is often referred to simply as the FLRW model (or the FRW model).